# Copyright © by Holt, Rinehart and Winston. All Rights Reserved. DO NOW: Solve for y. 1.4x – y = 7 2.x + 2y = 8 3.4 – 6y = 9x Y = 4x – 7 Y = -1/2x + 4 Y.

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Copyright © by Holt, Rinehart and Winston. All Rights Reserved. DO NOW: Solve for y. 1.4x – y = 7 2.x + 2y = 8 3.4 – 6y = 9x Y = 4x – 7 Y = -1/2x + 4 Y = -3/2x + 2/3

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Terms System of Equations: two equations in two variables. Solution to a System: ordered pair that is a solution to all equations in the system. The answer to a system is the point of intersection for the two lines! Graphing Systems of Equations

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Graphing Systems of Equations Graphing a system. Let’s take a look. 3x – 2y = 2 2x – 3y = 8 3 2 y = x – 1 2 3 y = x – 8 3 TOC

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Ex. 1) Solve the system by graphing. Graph paper and a ruler is needed to give the most accurate answer! Make sure both equations are in SLOPE-INTERCEPT form for easy graphing! Graph both lines. At what point do the two lines intersect?

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Y = 3x + 1 Y = -x + 5 Since (1,4) is the intersection, this is the ordered pair that is a solution to both lines; therefore, it is THE answer to the system! How can you check yourself? SUBSTITUE (1,4) in both equations to make sure its TRUE. 4 = 3(1) + 1 true 4 = -(1) + 5 true

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Ex 2) Solve the system of equations by graphing. Remember if your equations are NOT in slope intercept form (y = mx + b), you must make it that way! Graph both lines. What is the intersection? Check by substitution.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Y = 2x + 2 Y = -x - 1 Where do they intersect? The solution is (-1, 0) Use substitution to check! 0=2(-1) + 2 true 0= -(-1)-1 true

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Ex. 3) Change both to slope- intercept form. Graph both lines on a common coordinate plane to find a common solution.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Y = -3x + 4 Y = 1/2x - 3 The solution to the system is (2, -2) Check your answer. 3x + y =4 3(2) + (-2) = 4 6 – 2 = 4 true x – 2y = 6 2 – 2(-2) = 6 2 + 4 = 6 true

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Ex 4) Solve by graphing. Solve for y. Use slopes and intercepts to graph on common plane. Where do they intersect?

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Y = -2x + 2 Y = -x + 1 The solution to the system is (1, 0) Check by substitution! y + 2x = 2 0 + 2(1) = 2 true y + x = 1 0 + 1 = 1 true

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Summarizer When solving systems of equations by graphing, WHY do we need to make sure each equation of a line is in slope-intercept form? How do you check your answer from the graph? Why is it important to do this? So you can see the slope and intercept! Substitute the ordered pair into the system! IN case your graph is a little inaccurate, you can see the mistake !